Question

In the figure shown, find the velocity acquired by the block on reaching the ground and the force exerted by the inclined plane on the block if takes 5 seconds for the block to reach the ground. Assume all surfaces to be smooth. (Take $g=10m/s^2)$

• A. $10m/s,10\sqrt{3}N$
• B. $20m/s,10N$
• C. $25m/s,20N$
• D. $25m/s,10\sqrt{3}N$

Answer 1

The correct option is D $25m/s,10\sqrt{3}N$

To find the velocity of the block when it reaches the ground, we need to find the acceleration of the block along the incline plane,
FBD of the block will be,

Force on the body along the plane $=mgsin\theta$
$⟹$ acceleration =$\frac{mgsin\theta }{m}=gsin\theta$
Using second equation of motion, we can say
$v=u+at$
$v=0+gsin\theta t$
$⟹v=5\times 5=25m/s$
As there is no motion of the block along the direction perpendicular to the plane . So, $N=mgcos\theta$
$⟹N=20cos{30}^{\circ }$
$⟹N=10\sqrt{3}$ N